I've enjoyed talking about a lot of very common logical fallacies, but today I want to go slightly more obscure (inspired by yesterday's comments): the fallacy of sunk costs and its close relative the Monte Carlo fallacy. Both fallacies proceed from the same basic – and utterly flawed – premise. They assume that the probabilities or outcomes of independent events are somehow dependent.
The sunk costs fallacy is simply the belief that having already invested x to accomplish y logically supports the idea of investing more irrespective of whether or not it will contribute to accomplishing y. This is sometimes known as the "Concorde Fallacy" after a famous academic paper that used that ill-fated aircraft as a perfect example. Both investing nations (Britain and France) knew perfectly well that the plane was an albatross with no chance to be financially viable, but….they had already invested so goddamn much in its development that they believed the only logical thing to do was spend more to finish it. I think "good money after bad" is the proper adage. In other words, "If we stop now, all that we have spent will be lost."
This logic need not always be fallacious. If spending a few more bucks would have made the Concorde a money-making airplane, then additional spending would clearly be the best choice. To put it another way, let's say you're done with 2.5 years of law school. Stopping is a poor decision. Your investment will be lost – spending money for one more semester is the only smart choice. But suppose that after 3 years of law school you had not managed to pass a single class or accumulate a single credit. You're no closer to the goal than you were at the beginning. Unless you have some explicit reason to think that the 7th semester will be a success whereas the first 6 availed you of nothing, investing more is retarded.
Examples of this are far too common in the political world. We need not think back very far to find images of LBJ hemmoraging money and lives into Vietnam well after he explicitly concluded that the cause was hopeless. In more recent times, of course, Our President constantly tells us with respect to Iraq:
I've met too many wives and husbands who've lost their partner in life, too many children who'll never see their mom or dad again. I owe it to them and to the families who still have loved ones in harm's way, to ensure that their sacrifices are not in vain.
Look at that. It says absolutely nothing about how likely success is, or if we are any closer to success than we were in 2002. It is simply, "If we quit now, all we have invested will be lost." Which is, you know, the f'n definition of this fallacy. If you are wasting or have wasted something, the proper response is to stop. Instead, they spend more in a Quixote-like quest to change what has already happened. If there is a reason to believe that spending more will affect the outcome, then by all means go ahead. But an argument based on spending more to honor or justify what has already been spent is…is "idiotic" too strong of a word? There's a reason that every stock market investor who subscribes to this logic goes broke.
One often finds this paired with the Monte Carlo fallacy (aka "Gambler's Fallacy"). This is simply a belief that independent events are not independent. If I flip a coin 10 times and get 10 heads, it is still 50/50 that the 11th toss will be tails. It is not more likely to be heads because the coin has produced 10 consecutive heads. Gamblers believe in things like "runs" of events and completely disregard the fact that most of what they do (roulette wheel spins, for example) are entirely independent. Your odds for red vs. black on any roulette wheel spin are 18/38. It doesn't matter if it's the first spin or the 10,000th spin – that is the probability. Period. Two blacks in a row or two thousand blacks in a row are irrelevant.
The logic of allocating resources depends solely on an objective analysis of the facts. Will the expenditure contribute to accomplishing the goal? What are the actual odds of success? Instead, partly out of stubbornness and partly out of abject stupidity, people abandon all logic in favor of emotion. They're humiliated by failure and embarassed to be wrong so they rationalize proceeding when all signs say "stop." All of these arguments – we're "due," we're on a hot streak, or we must keep spending because we've already spent a lot – are branches of the same tree. And all of them are the kind of thing that enable stupid people to turn ordinary setbacks into crippling, spectacular failures.